An ecosystem model is a representation of an ecosystem shown in mathematical form. Such models are used in theoretical ecology to help ecologists study existing ecosystems and predict what might happen given certain conditions. A ecosystem is incredibly complex, so an ecosystem model generally must simplify the system by focusing only on specific parts.

Ecosystems are biological environments. They include all living creatures in a particular area as well as the physical characteristics of that area that might affect or be used by the organisms in it. These could be such things as air, water or amount of sunlight. The model must also take into account the size of the environment being studied since this may have an effect on the organisms in it.

In order to create a workable mathematical model, an ecologist must simplify the ecosystem he or she is trying to study. This can be done by focusing on a limited number of species or groups that share certain traits. These traits could be behavioral, biochemical or physical.

Once the ecologist has isolated the organisms of interest, he or she creates a food chain for them. A food chain is a representation of predator-prey relationships. For example, if the animal of interest is the coyote, the food chain might show that the coyote eats rabbits, which eat ground level vegetation. The coyotes, the rabbits and the vegetation will all become elements in the ecosystem model.

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The elements in the ecosystem model are then linked together using mathematical functions that describe their relationships. Again the complexity of an ecosystem presents a problem for the ecologist. It is difficult to observe what actual affect the consumption of a single rabbit will have on the coyote population, so ecologists use statistics, observation and other methods to arrive at an educated guess. Mathematical functions can be adjusted as real events in the ecosystem prove or disprove the accuracy of the ecosystem model.

A classic ecosystem model studied by ecology students is the predator-prey model created in the mid 1920s. It was created independently by two scientists in the space of one year: US mathematician, chemist and statistician Alfred J Lotka and Italian mathematician and physicist Vito Volterra. Their model uses a pair of differential equations to represent predators and prey. Though originally used to describe fluctuations in shark and fish populations in the Adriatic Sea, the model works as a general description of the predator-prey relationship.

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